III. Encuentre la derivada direccional de la función en P en dirección de Q 11. f(x,y) = x² + 4y², P(3,1), Q(1,-1)

Q: 3. Find fz and fy where f(x,y) = In(x + y²).

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Q: 2. Show that the function u = p(xy) + Vry (y/x) provides the equation y². 0. dy?

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Q: De min Jx when f(x, y) = cos(y – x) – x sin(y – x). 1. fr = -x sin(y – x) | 2. fa = x sin(y – x) 3.…

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Q: 7-The tangent of the curve x^2+y^2- 2xy3D0 at the point (1,1), is * O a. y=2-x. O b. y=x-2. C.…

A: We find equation of tangent to the curve

Q: -Find the D.f ofr (x, y) = (x² – y)' at Po(3, 1) with

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Q: Find the derivatie: F (+2 %3D (-t*+*z+)た =人

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Q: 2Use divectional devivative delinihion of f(Hiy)=x y'at the divecionof ū =i jatthe Point (le2>

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Q: 2. Find a function f(x, y) which is NOT linear in either a or y and for which the tangent plane at…

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Q: Determine (x, y) and 2(x, y), where f(x, y) = X sen(xy) %3D y

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Q: 2z Forz> 0, 순(/"m(P + 1) a) In (t³ + 1) dt For x > 0,

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Q: 2. Show that the function u = (xy) + JTY v(y/x) provides the equation y² : 0. dy?

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Q: 2. Show that the function u = p(xy) + Vry ý(y/x) provides the equation n, = 0. dy? U -

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Q: 3. Find the interval on which the curve of y= 2 1+3t+t² dt is concave up.

A: Second derivative is positive.

Q: Use a linear approximation to estimate f(0,1), given that y=f(X) is a differentiable  with f(0)=1…

A: Consider the given information

Q: 6) If y=x² +1+ f dt , prove that y"= 2 - x2

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Q: ) Find the linearization of f(x) = sinx at x = 0.(b) Compute dy if y = x2 +x and x changes from x =…

A: Since you have submitted two questions, we'll answer the first question. For the second question…

Q: 18. Use the Linear Approximation to f(x, y) = /x/y at (9,4) to estimate 19.1/3.9.

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Q: If f(x,y,z) = z In(x²ycosz): then fz is

A: Here, the given function is: f(x,y,z)=z ln(x2ycos z) Using the properties of the natural logarithm:…

Q: What does it mean for the differentiability of a function if only one of the Cauchy-Reimann…

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Q: 2 Find f, fyand f. if f(x, y, z) = x-Vy + z°

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Q: Find fr and fy- f (x, y): 6e dt 4 fa(x, y) = fy(x, y) =

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Q: 8.xy² If u = and error in x, y, z be 0.001, compute the maximum absolute and relative z³ error, when…

A: Given equation be u=8xy2z3 error in x, y, z be 0.001 Now ∂u∂x=8y2z3, ∂u∂y=16xyz3, ∂u∂z=-24xy2z4  and…

Q: The antiderivative of the function 4 .3 + 10x³ is, 4 f(x) - -4 .3 + 2.5x³ + c 4 -10 + 1.0xª + c -4 +…

A: According to question given f(x)=44.3+10x3We have to calculate the antiderivative

Q: Find f, and f, for f(x,y)=y In (3x +4y). fx fy

A: When the partial differentiation is done with respect to a specific variable, then all other…

Q: Let f (x, y) = 2x³ + 4y³ + 19xy Find D = frx · fyy - fey at the point (2,2)

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Q: prove that xy^2/x^2+y^2 is not differentiable at 0,0 when  xy^2/x^2+y^2 if (x,y) not equal to (0,0)…

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Q: 2. Find whether the function F-(* - y' )i + (v² - 3x)j + (:² - xy is irrotational.

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Q: Find fr, fy, and fz. f(x, Y, z) = 4yz In(6ry) fz = fy = f: =

A: Given: f(x, y, z)=4yz ln(6xy)

Q: Verify Young's Theorem S. f(x, y) = = e(2x+y) In(xy)

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Q: 5.) Use linear approximation to estimate f(0.1, −0.9) x² sin x In(y² + 1) Y f(x, y) = of th + x+1…

A: NOTE: Refresh your page if you can't see any equations. . here we want to find the approximate…

Q: Encuentre máximo(s) y/o mínimo(s) relativos de f(x) = 1- 5z2 +4. (Si es que estos existen).…

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Q: 3. Determine if (х — 1)2, if x 1 is differentiable at x = 1.

A: Given  hx=x-12if x≤1x-1if x>1

Q: Display the values of the functions in Exercises 37–48 in two ways:(a) by sketching the surface z =…

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Q: - Given f(x, y, z) = x In(yz³), find fzy and fyz.

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Q: Verify Young's Theorem f(x,y) = e(2x+y) In(xy)

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Q: (ii)If y=(x+Jx* +1. prove that y'= Vx +1

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Q: 3. Evaluate the gradient of S(1, y, 2) = In(cosh z+ y) - arctan| at (1,y) = (7/2, 1).

A: Given that fx,y,z=lncosh x+y-z2 arctanx2y2+z2 To find the gradient of f(x,y,z) :…

Q: 8. Find the directional derivative of f (x, y, z) = xy²z³ at P(2,1,1) in the direction of Q(0, –3,5)

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Q: Obtain the orthogonal trajectories of y=Cx^2 and compute for the positive value of y of the…

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Q: Integrate from f(x) = x4 from 0 to 1 by (Trapezoidal Rule) with h = 1, h = 0.5, h = 0.25 and…

A: Here, f(x)=x⁴ So, I=  Integrate from f(x) = x⁴ from 0 to 1. Now we can solve by Trapezoidal rule,…

Q: If ƒf (x) =¸ (A) (B) Sº sec²x 1+elanx In (secx) √✓ 1+tan²x tanx 1+e sec ³x tanx 1+e 1+1² tanx…

A: Using Leibnitz integral rule.

Q: At what interval is y=2r4- 4x2 concave upward? U x> 3 x 3 3 <x<- 3 3

A: The given function is y=2 x4-4 x2 We have to find the interval at which the function is concave…

Q: Show that the function f(x, y) = 3x - 4y² is differentiable at point (−1, 2)

A: answer is in next step. please give a like !!!

Q: 2. Let f(x,y) 3x y. If C is the line segment from (1,1) to (2,3), evaluate r'dt.

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Q: xyz f(x.y.z) = et ot function is given P(2,,4) in point fux + fyy + fzz colculate.

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Q: Let y = 5x² + 4x + 4. If Ax = 0.3 at x = 4, use linear approximation to estimate Ay Ay ~ Submit…

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Q: (b) Show that the function defined by xy √√√²+y² f(x, y) 0 if (x, y) = (0,0) is not differentiable…

A: We have to show that the function defined by…

Q: 9. If f(x,y) = -cos x+e*y, find Vf(x, y).

A: For the solution follow the next step.

Q: (6) Find the orthogonal trajectories of the family of curves r= 2C sin 0, where C being parameter.

A: See the detailed solution below.